Abstract
M. Numata described edge regular graphs without 3-stars. Allμ-subgraphs of these graphs are regular of the same valency. We prove that a connected graph without 3-stars all of whoseμ- subgraphs are regular of valencyα > 0 is either a triangular graph, or the Shläfli graph, or the icosahedron graph.
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Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 407–413, March, 1998.
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Makhnev, A.A. On a class of graphs without 3-stars. Math Notes 63, 357–362 (1998). https://doi.org/10.1007/BF02317782
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DOI: https://doi.org/10.1007/BF02317782